Question:
If a,b,c are real numbers then the roots of the equation
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are always
If a,b,c are real numbers then the roots of the equation
(x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0
are always
Show Hint
Symmetric expressions in real numbers usually give real roots.
Updated On: Mar 19, 2026
- real
- imaginary
- positive
- negative
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The Correct Option is A
Solution and Explanation
Simplifying the equation gives a quadratic with real coefficients and non-negative discriminant.
Hence, roots are always real.
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